According to the traditional circuit theories, resistors, capacitors and inductors are three fundamental circuit elements, wherein, the resistors are defined by the current-voltage conversion relationship, the capacitors are defined by the voltage-charge conversion relationship, and the inductors are defined by the current-magnetic flux conversion relationship. In 1971, Leon Chua of the University of California, USA proposed theoretically, based on the concept of symmetry, that there should be a fourth fundamental circuit element, which is defined by the conversion relationship between charge and magnetic flux (cf. Memristor—the missing circuit element, IEEE Transactions on Circuit Theory; Vol. 18, Pages 507-519, 1971) as shown in Formula (1). At that time, no physical example about charge-magnetic flux conversion was found, and thus Leon Chua took derivatives of both sides of Formula (1) with respect to time t and obtained Formula (2), and further obtained Formula (3). However, a circuit element M defined by Formula (3) is equivalent to a resistor R, and therefore is not meaningful. In order to make M different from conventional resistors, Leon Chua assumed that M can be a variable depending on charge q and time t, rather than a constant, and thus obtained Formula (4). In this case, a nonlinear resistive element, dubbed memristor, can be defined from Ohm's law as in Eq. (4).
                              d          ⁢                                          ⁢          φ                =                  M          ⁢                                          ⁢          dq                                    (        1        )                                                      d            ⁢                                                  ⁢            φ                    dt                =                  M          ⁢                      dq            dt                                              (        2        )                                v        =                  Mi                      v            =            Mi                                              (        3        )                                          v          ⁡                      (            t            )                          =                              M            ⁡                          (                              q                ⁡                                  (                  t                  )                                            )                                ⁢                      i            ⁡                          (              t              )                                                          (        4        )            
Nearly 40 years after the proposal of this theory, researchers of Hewlett-Packard Company found that a simple Pt/TiO2/Pt sandwich structure presents an i-v curve similar to that of a theoretically predicted memristor, and declared that a memristor was found experimentally (cf. The missing memristor found, D. B. Strukov, G. S. Snider, D. R. Stewart, R. S. Williams, Nature, Vol. 453, Pages 80-83, 2008).
Although the memristor has an important application prospect due to its non-linear memory function, it cannot be regarded as a true fourth fundamental circuit element. Firstly, the memristor does not satisfy the original definition of the fourth fundamental element (Formula (1)). In other words, the memristor is not defined directly by the conversion relationship between charge and magnetic flux. Secondly, the memristor is essentially a resistance device, with the operation and action thereof being completely independent of the magnetic flux, and having no magnetic flux memory function. Thirdly, the memristor as a non-linear device is unequal in status to the other three linear fundamental elements, resulting contradictions in fundamental circuit theories. Finally, since the memristor is essentially a resistance device, which has a high operation power consumption and is very different from ideal charge-magnetic flux conversion devices with low power consumption, the application thereof is very limited. Therefore, the fourth fundamental circuit element strictly satisfying the original definition for directly realizing charge-magnetic flux conversion is still missing.